{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:KBF3OB6CEQ3A6DKT2QJMQTJNQ7","short_pith_number":"pith:KBF3OB6C","canonical_record":{"source":{"id":"1208.0790","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-03T16:33:21Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"4d22ba890b3f977fe8a52d0cb2a6aee310ac85ea431a9d744c0396c987ebf778","abstract_canon_sha256":"28ef9fe0159a9ab7c5ee089dd68e2cb269da98ab6e82de5891ca956cc6af3270"},"schema_version":"1.0"},"canonical_sha256":"504bb707c224360f0d53d412c84d2d87fca374fe2a67fd37e5017b187041f60a","source":{"kind":"arxiv","id":"1208.0790","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0790","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0790v4","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0790","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"pith_short_12","alias_value":"KBF3OB6CEQ3A","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KBF3OB6CEQ3A6DKT","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KBF3OB6C","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:KBF3OB6CEQ3A6DKT2QJMQTJNQ7","target":"record","payload":{"canonical_record":{"source":{"id":"1208.0790","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-03T16:33:21Z","cross_cats_sorted":["math-ph","math.AG","math.MP"],"title_canon_sha256":"4d22ba890b3f977fe8a52d0cb2a6aee310ac85ea431a9d744c0396c987ebf778","abstract_canon_sha256":"28ef9fe0159a9ab7c5ee089dd68e2cb269da98ab6e82de5891ca956cc6af3270"},"schema_version":"1.0"},"canonical_sha256":"504bb707c224360f0d53d412c84d2d87fca374fe2a67fd37e5017b187041f60a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:23.261206Z","signature_b64":"KCg+ivGFwHizHHkkVDjxnjcy+a4Fk/I0zCJ5A3x4OwZYsQeke21oUs6tI87rb8Qkep1+X8s8dFDV3EqghIhTBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"504bb707c224360f0d53d412c84d2d87fca374fe2a67fd37e5017b187041f60a","last_reissued_at":"2026-05-18T01:55:23.260586Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:23.260586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1208.0790","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3i97vjTl2es6NxVRB7uCj11ECoXzvjRyTl0yDTKE1q2d0fJoUbeZGzxqeKKWhuBot1v6bySEa+jVtGZhZLvRAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T19:22:13.172249Z"},"content_sha256":"1d82d4813a2618e894e09aba4a576a542f4fb6996798fc01a977f65eb896774a","schema_version":"1.0","event_id":"sha256:1d82d4813a2618e894e09aba4a576a542f4fb6996798fc01a977f65eb896774a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:KBF3OB6CEQ3A6DKT2QJMQTJNQ7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP"],"primary_cat":"hep-th","authors_text":"Alessandro Tanzini, Futoshi Yagi, Giulio Bonelli, Kazunobu Maruyoshi","submitted_at":"2012-08-03T16:33:21Z","abstract_excerpt":"We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2 \\to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety.We provide a check of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0790","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:55:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mPwlolJydxRNN98YKtniD3HoIpg8ZnkM5JbvdYWc+PxjHm1BZZ8w4d0KLz6V5u8ycYbP0i6z14Ah1GJHorTgDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T19:22:13.172928Z"},"content_sha256":"e48aac211c49c464869ec07461d19f3b345545fc528dffc5434da223d5f7bd99","schema_version":"1.0","event_id":"sha256:e48aac211c49c464869ec07461d19f3b345545fc528dffc5434da223d5f7bd99"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7/bundle.json","state_url":"https://pith.science/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-19T19:22:13Z","links":{"resolver":"https://pith.science/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7","bundle":"https://pith.science/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7/bundle.json","state":"https://pith.science/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KBF3OB6CEQ3A6DKT2QJMQTJNQ7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:KBF3OB6CEQ3A6DKT2QJMQTJNQ7","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"28ef9fe0159a9ab7c5ee089dd68e2cb269da98ab6e82de5891ca956cc6af3270","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-03T16:33:21Z","title_canon_sha256":"4d22ba890b3f977fe8a52d0cb2a6aee310ac85ea431a9d744c0396c987ebf778"},"schema_version":"1.0","source":{"id":"1208.0790","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1208.0790","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"arxiv_version","alias_value":"1208.0790v4","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.0790","created_at":"2026-05-18T01:55:23Z"},{"alias_kind":"pith_short_12","alias_value":"KBF3OB6CEQ3A","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"KBF3OB6CEQ3A6DKT","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"KBF3OB6C","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:e48aac211c49c464869ec07461d19f3b345545fc528dffc5434da223d5f7bd99","target":"graph","created_at":"2026-05-18T01:55:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We compute the Nekrasov partition function of gauge theories on the (resolved) toric singularities C^2/\\Gamma in terms of blow-up formulae. We discuss the expansion of the partition function in the \\epsilon_1,\\epsilon_2 \\to 0 limit along with its modular properties and how to derive them from the M-theory perspective. On the two-dimensional conformal field theory side, our results can be interpreted in terms of representations of the direct sum of Heisenberg plus W_N-algebrae with suitable central charges, which can be computed from the fan of the resolved toric variety.We provide a check of t","authors_text":"Alessandro Tanzini, Futoshi Yagi, Giulio Bonelli, Kazunobu Maruyoshi","cross_cats":["math-ph","math.AG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-03T16:33:21Z","title":"N=2 gauge theories on toric singularities, blow-up formulae and W-algebrae"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.0790","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1d82d4813a2618e894e09aba4a576a542f4fb6996798fc01a977f65eb896774a","target":"record","created_at":"2026-05-18T01:55:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"28ef9fe0159a9ab7c5ee089dd68e2cb269da98ab6e82de5891ca956cc6af3270","cross_cats_sorted":["math-ph","math.AG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-08-03T16:33:21Z","title_canon_sha256":"4d22ba890b3f977fe8a52d0cb2a6aee310ac85ea431a9d744c0396c987ebf778"},"schema_version":"1.0","source":{"id":"1208.0790","kind":"arxiv","version":4}},"canonical_sha256":"504bb707c224360f0d53d412c84d2d87fca374fe2a67fd37e5017b187041f60a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"504bb707c224360f0d53d412c84d2d87fca374fe2a67fd37e5017b187041f60a","first_computed_at":"2026-05-18T01:55:23.260586Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:55:23.260586Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KCg+ivGFwHizHHkkVDjxnjcy+a4Fk/I0zCJ5A3x4OwZYsQeke21oUs6tI87rb8Qkep1+X8s8dFDV3EqghIhTBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:55:23.261206Z","signed_message":"canonical_sha256_bytes"},"source_id":"1208.0790","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1d82d4813a2618e894e09aba4a576a542f4fb6996798fc01a977f65eb896774a","sha256:e48aac211c49c464869ec07461d19f3b345545fc528dffc5434da223d5f7bd99"],"state_sha256":"6694be1c52833e8c691ae330b473a4d120cb49f7034c11d7e57850cf3db53d38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofnc1sSschC8MNvEiKlFLD1PDHOE96zjKa5GEDOOV41sg5NtlA49vHfyg+zGTsOtkm9MjYHjAO1LjwwRsUVSAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T19:22:13.179894Z","bundle_sha256":"437422cc1722de55d34847f18adc0f433762a3241958077f6583115b93bbcbb2"}}